MinT - Best Known (149−43, 149, s)-Nets in Base 3

Best Known (149−43, 149, s)-Nets in Base 3

(149−43, 149, 228)-Net over F₃ — Constructive and digital

Digital (106, 149, 228)-net over F₃, using

1 times m-reduction [i] based on digital (106, 150, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 50, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(149−43, 149, 394)-Net over F₃ — Digital

Digital (106, 149, 394)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−43, 149, 9980)-Net in Base 3 — Upper bound on s

There is no (106, 149, 9981)-net in base 3, because

1 times m-reduction [i] would yield (106, 148, 9981)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41175 407785 876728 910935 950130 759391 224155 769942 489907 310977 307837 218251 > 3¹⁴⁸ [i]